Depending on the type of check, it will. However, depending on your state, it may have gone off your record after a certain amount of time- check with your registry.
A DUI will show on your record. An employer may be willing to excuse this past infraction provided that the applicant was truthful regarding the matter.
I think it will show up. Because it was an arrest so yes. You would need to say if you were ever arrest for anything. But you should ask a lawyer to find out more. But if you are honest with your employer it should be a problem with them.